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Similarity, Right Triangles, and Trigonometry


Standards in this domain:

Understand similarity in terms of similarity transformations

  • HSG-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor:
    • A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
    • The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
  • HSG-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  • HSG-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Prove theorems involving similarity

  • HSG-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
  • HSG-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Define trigonometric ratios and solve problems involving right triangles

  • HSG-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
  • HSG-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.
  • HSG-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Apply trigonometry to general triangles

  • HSG-SRT.D.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
  • HSG-SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
  • HSG-SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Printed from the Iowa Department of Education website on April 16, 2014 at 9:34am.